Successful structure learning from observational data

Abstract

Previous work suggests that humans find it difficult to learn the structure of causal systems given observational data alone. We identify two conditions that enable successful structure learning from observational data: people succeed if the underlying causal system is deterministic, and if each pattern of observations has a single root cause. In four experiments, we show that either condition alone is sufficient to enable high levels of performance, but that performance is poor if neither condition applies. A fifth experiment suggests that neither determinism nor root sparsity takes priority over the other. Our data are broadly consistent with a Bayesian model that embodies a preference for structures that make the observed data not only possible but probable.

Introduction

Causal networks have been widely used as models of the mental representations that support causal reasoning. For example, an engineer’s knowledge of the local electricity system may take the form of a network in which the nodes represent power stations and the links in the network represent connections between stations. Causal networks of this kind may be learned in several ways. For example, an intervention at station A that also affects station B provides evidence for a directed link between A and B. Networks can also be learned via instruction: for example, a senior colleague might tell the engineer that A sends power to B. Here, however, we focus on whether and how causal networks can be learned from observational data. For example, the engineer might observe that A and B both have voltage spikes on some occasions, that B alone has voltage spikes on others, but that A is never the only station with voltage spikes (Fig. 1). Based on these observations alone, the engineer might infer that A sends power to B.

The problem in Fig. 1 is an instance of structure learning because it requires a choice between two distinct graph structures: one in which A sends a link to B and the other in which B sends a link to A. Structure learning can be distinguished from parameter learning problems that require inferences about the properties of links in a known causal structure (Danks, 2014, Jacobs and Kruschke, 2011). For example, an engineer who knows that station A sends a link to station B might need to learn about the fidelity with which signals at A are transmitted to B. Causal parameter learning is often studied experimentally using paradigms in which a focal effect is clearly distinguished from a set of potential causes, and the learning problem is to infer the strength of the relationship between each candidate cause and the effect (Lu et al., 2008, Sloman, 2005). Here, however, we focus on structure learning problems in which the variables are not presorted into potential causes and effects.

A consensus has emerged that people find causal structure learning to be difficult or impossible given observational data alone. For example, Fernbach and Sloman (2009) cite results obtained by Steyvers et al., 2003, Lagnado and Sloman, 2004, White, 2006 to support their claim that “observation of covariation is insufficient for most participants to recover causal structure” (p. 680). Here we challenge this consensus by identifying two conditions that enable successful structure learning from observational data alone. The first condition is causal determinism, and is satisfied if each variable is a deterministic function of its direct causes. The second condition is root sparsity, and is satisfied if each observation is the outcome of a single root cause. Both conditions simplify the structure-learning problem by reducing the number of possible explanations for a given set of observations.

Determinism and root sparsity have both previously been discussed in the literature on causal reasoning. Several lines of research suggest that people tend to assume that causes are deterministic or near-deterministic (Frosch and Johnson-Laird, 2011, Lu et al., 2008, Schulz and Sommerville, 2006, Yeung and Griffiths, 2015), and this assumption has informed previous studies of structure learning (Mayrhofer and Waldmann, 2011, Mayrhofer and Waldmann, 2016, White, 2006). Our work is related most closely to a previous study by White (2006), who asked participants to learn the structure of deterministic causal systems from observational data alone. White’s task proved to be difficult, and performance was poor even when White gave his participants explicit instructions about how to infer causal structure from observational data. In contrast, we find that our participants are reliably able to infer the structure of deterministic causal systems.

Although “root sparsity” is our own coinage, this term is related to a cluster of existing ideas. Some work on causal attribution suggests that people tend to prefer explanations that invoke a single root cause (Chi et al., 2012, Lombrozo, 2007, Pacer and Lombrozo, 2017), although Zemla, Sloman, Bechlivanidis, and Lagnado (2017) report the opposite finding. Many studies of causal parameter learning consider cases in which there are two potential causes of an effect: a focal cause and a background cause. In this setting learners seem to expect that exactly one of these potential causes is strong (Lu et al., 2008). Mayrhofer and Waldmann (2015) explore a related idea in their work on prior expectations in structure learning. One of the priors that they consider captures the idea that an effect has a single cause. The notion of root sparsity is also consistent with studies of structure learning that focus on the role of interventions. Several researchers in this literature suggest that people tend to succeed only when interventions are not accompanied by spurious changes. If this condition holds then all changes observed following an intervention can be traced back to a single root cause – that is, to the intervention (Fernbach and Sloman, 2009, Lagnado and Sloman, 2004). Rottman and Keil (2012) show that the same condition supports structure learning from observational data if the temporal sequence of the observations is known.

Our primary goal is to explore the extent to which determinism and root sparsity allow people to succeed at structure learning. We find that people perform well when determinism and root sparsity both apply, and that either condition alone is sufficient to produce high levels of performance. To help us understand our participants’ inferences, we compare these inferences to the predictions of several computational models. We initially focus on a model that we refer to as the Bayesian structure learner, or the BSL for short. The BSL serves as a normative benchmark that helps to evaluate the extent to which people succeed at structure learning. Previous discussions of structure learning have also considered Bayesian benchmarks, but Fernbach and Sloman (2009) suggest that there is “little reason to treat them as descriptively correct” (p. 681). In our setting, however, we find that people’s inferences align closely with the predictions of our Bayesian model in many cases.

The BSL model contrasts with previous statistical accounts of structure learning that are sensitive to patterns of conditional independence between variables (Pearl, 2000, Spirtes et al., 2001). Like several previous authors (Fernbach and Sloman, 2009, Mayrhofer and Waldmann, 2011), we believe that models that track patterns of conditional independence are often too powerful to capture inferences made by resource-bounded human learners. The BSL model uses statistical inference in a different way, and relies on a computation that assesses how much of a coincidence the available data would be with respect to different possible structures. It is therefore possible that people rely on a similar kind of statistical computation when approaching structure learning problems.